</sarcasm>
That said, this does bring to mind one genuinely useful aspect to the blockchain I forgot about, and that's the fact that Keybase uses the bitcoin blockchain (IIRC) to periodically record the Merkle tree roots that they use to verify their own information. The only reason to do this is as proof that they're not tampering with the Keybase history that they publish, and so fundamentally this is just the same thing as digital notarizing that I did mention before (except in this case it doesn't matter whether the courts recognize it as being valid). And you could still accomplish this without a blockchain simply by having a neutral third party agree to keep a record of the merkle tree roots, but this is one of the few cases where the 'trustless' aspect of the blockchain actually is useful.
Though of course even with a 'trustless' blockchain you still have to trust the chain itself. With Bitcoin, you can assume nobody's managed to execute a 51% attack against the chain (at least, for the time being; AIUI with the way things are going it looks like the Chinese government might be able to do it by exerting pressure on all the Chinese miners), but if you're running your own chain, how do you make mining the chain popular enough to prevent attacks?
In fact, to my mind, the only real benefit of Bitcoin at this point is the fact that it's so popular it's hard to attack (well, except by the Chinese government).
I'm not actually a Bitcoin/blockchain hater; I can't avoid having a soft spot for any tech that makes me feel like I'm living in a cyberpunk world :) What I dislike is the mania. Bitcoin is a cool experiment, not a production-ready solution to anything.
Say the manufacturer instead just has an RSS feed on their site, where they publish that information (digitally signed, of course) as the milk is produced. The retailers just have to keep a local copy of that feed, and so they can detect any later tampering.